A-LevelMathematicsMechanics9709/43 · Oct/Nov 2017 · Q69 Marks

The diagram shows the velocity-time graphs for two particles, P and Q, which are moving in the same straight line. The graph for P consists of four straight line segments. The graph for Q consists of three straight line segments. Both particles start from the same initial position O on the line. Q starts 2 seconds after P and both particles come to rest at time t = T. The greatest velocity of Q is V m s⁻¹.[Figure 6.1]

(i)Find the displacement of P from O at t = 10.[1]
(ii)Find the velocity of P at t = 12.[2]
(iii)Given that the total distance covered by P during the T seconds of its motion is 49.5 m, find the value of T.[3]
(iv)Given also that the acceleration of Q from t = 2 to t = 6 is 1.75 m s⁻², find the value of V and hence find the distance between the two particles when they both come to rest at t = T.[3]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

[Area = ½ (10 + 4) × 6 = 42 m] B1
Displacement = 42 m
v = 6 / 2 * 4 M1 Using similar triangles or using acceleration = gradient and v = u + at
or [gradient =1.5, v = 6 + 1.5 × 6]
v = 3 ms⁻¹ A1
Total distance travelled = 42 + ½ (T-10) × 3 B1 FT Area found with FT distance from (i) and FT speed from (ii)
[42 + ½ (T− 10) × 3 = 49.5] →T= ... M1 For equation and solving for T
T = 15 s A1
V = 1.75 × 4 = 7 ms⁻¹ B1
Q travels [½ (13 + 6) × 7 = 66.5 m] M1 Finding area for Q and interpreting total distance between particles
Distance apart = [66.5 + 42 – 7.5]
Distance between P and Q = 101 m A1

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.